Mr. Ellison believed that Mr. Obama’s message of unity resonated deeply with American Muslims. He volunteered to speak on Mr. Obama’s behalf at a mosque in Cedar Rapids, one of the nation’s oldest Muslim enclaves. But before the rally could take place, aides to Mr. Obama asked Mr. Ellison to cancel the trip because it might stir controversy. Another aide appeared at Mr. Ellison’s Washington office to explain.

“I will never forget the quote,” Mr. Ellison said, leaning forward in his chair as he recalled the aide’s words. “He said, ‘We have a very tightly wrapped message.’ ”

When Mr. Obama began his presidential campaign, Muslim Americans from California to Virginia responded with enthusiasm, seeing him as a long-awaited champion of civil liberties, religious tolerance and diplomacy in foreign affairs. But more than a year later, many say, he has not returned their embrace.

While the senator has visited churches and synagogues, he has yet to appear at a single mosque. Muslim and Arab-American organizations have tried repeatedly to arrange meetings with Mr. Obama, but officials with those groups say their invitations — unlike those of their Jewish and Christian counterparts — have been ignored. Last week, two Muslim women wearing head scarves were barred by campaign volunteers from appearing behind Mr. Obama at a rally in Detroit.

In interviews, Muslim political and civic leaders said they understood that their support for Mr. Obama could be a problem for him at a time when some Americans are deeply suspicious of Muslims. Yet those leaders nonetheless expressed disappointment and even anger at the distance that Mr. Obama has kept from them.

“This is the ‘hope campaign,’ this is the ‘change campaign,’ ” said Mr. Ellison, Democrat of Minnesota. Muslims are frustrated, he added, that “they have not been fully engaged in it.”

Aides to Mr. Obama denied that he had kept his Muslim supporters at arm’s length. They cited statements in which he had spoken inclusively about American Islam and a radio advertisement he recorded for the recent campaign of Representative Andre Carson, Democrat of Indiana, who this spring became the second Muslim elected to Congress.

In May, Mr. Obama also had a brief, private meeting with the leader of a mosque in Dearborn, Mich., home to the country’s largest concentration of Arab-Americans. And this month, a senior campaign aide met with Arab-American leaders in Dearborn, most of whom are Muslim. (Mr. Obama did not campaign in Michigan before the primary in January because of a party dispute over the calendar.)

“Our campaign has made every attempt to bring together Americans of all races, religions and backgrounds to take on our common challenges,” Ben LaBolt, a campaign spokesman, said in an e-mail message.

Mr. LaBolt added that with religious groups, the campaign had largely taken “an interfaith approach, one that may not have reached every group that wishes to participate but has reached many Muslim Americans.”

The strained relationship between Muslims and Mr. Obama reflects one of the central challenges facing the senator: how to maintain a broad electoral appeal without alienating any of the numerous constituencies he needs to win in November.

After the episode in Detroit last week, Mr. Obama telephoned the two Muslim women to apologize. “I take deepest offense to and will continue to fight against discrimination against people of any religious group or background,” he said in a statement.

Such gestures have fallen short in the eyes of many Muslim leaders, who say the Detroit incident and others illustrate a disconnect between Mr. Obama’s message of unity and his campaign strategy.

“The community feels betrayed,” said Safiya Ghori, the government relations director in the Washington office of the Muslim Public Affairs Council.

Even some of Mr. Obama’s strongest Muslim supporters say they are uncomfortable with the forceful denials he has made in response to rumors that he is secretly a Muslim. (Ten percent of registered voters believe the rumor, according to a poll by the Pew Research Center.)

In an interview with “60 Minutes,” Mr. Obama said the rumors were offensive to American Muslims because they played into “fearmongering.” But on a new section of his Web site, he classifies the claim that he is Muslim as a “smear.”

“A lot of us are waiting for him to say that there’s nothing wrong with being a Muslim, by the way,” Mr. Ellison said.

Mr. Ellison, a first-term congressman, remains arguably the senator’s most important Muslim supporter. He has attended Obama rallies in Minnesota and appears on the campaign’s Web site. But Mr. Ellison said he was also forced to cancel plans to campaign for Mr. Obama in North Carolina after an emissary for the senator told him the state was “too conservative.” Mr. Ellison said he blamed Mr. Obama’s aides — not the candidate himself — for his campaign’s standoffishness.

Despite the complications of wooing Muslim voters, Mr. Obama and his Republican rival, Senator John McCain, may find it risky to ignore this constituency. There are sizable Muslim populations in closely fought states like Florida, Michigan, Ohio and Virginia.

In those states and others, American Muslims have experienced a political awakening in the years since Sept. 11, 2001. Before the attacks, Muslim political leadership in the United States was dominated by well-heeled South Asian and Arab immigrants, whose communities account for a majority of the nation’s Muslims. (Another 20 percent are estimated to be African-American.) The number of American Muslims remains in dispute as the Census Bureau does not collect data on religious orientation; most estimates range from 2.35 million to 6 million.

A coalition of immigrant Muslim groups endorsed George W. Bush in his 2000 campaign, only to find themselves ignored by Bush administration officials as their communities were rocked by the carrying out of the USA Patriot Act, the detention and deportation of Muslim immigrants and other security measures after Sept. 11.

As a result, Muslim organizations began mobilizing supporters across the country to register to vote and run for local offices, and political action committees started tracking registered Muslim voters. The character of Muslim political organizations also began to change.

“We moved away from political leadership primarily by doctors, lawyers and elite professionals to real savvy grass-roots operatives,” said Mahdi Bray, executive director of the Muslim American Society Freedom Foundation, a political group in Washington. “We went back to the base.”

In 2006, the Virginia Muslim Political Action Committee arranged for 53 Muslim cabdrivers to skip their shifts at Dulles International Airport in Northern Virginia to transport voters to the polls for the midterm election. Of an estimated 60,000 registered Muslim voters in the state, 86 percent turned out and voted overwhelmingly for Jim Webb, a Democrat running for the Senate who subsequently won the election, according to data collected by the committee.

The committee’s president, Mukit Hossain, said Muslims in Virginia were drawn to Mr. Obama because of his support for civil liberties and his more diplomatic approach to the Middle East. Mr. Hossain and others said his multicultural image also appealed to immigrant voters.

“This is the son of an immigrant; this is someone with a funny name,” said James Zogby, president of the Arab American Institute, who is a Christian who has campaigned for Mr. Obama at mosques and Arab churches. “There is this excitement that if he can win, they can win, too.”

Yet some Muslim and Arab-American political organizers worry that the campaign’s reluctance to reach out to voters in those communities will eventually turn them off. “If they think that they are voting for a campaign that is trying to distance itself from them, my big fear is that Muslims will sit it out,” Mr. Hossain said.

Throughout the primaries, Muslim groups often failed to persuade Mr. Obama’s campaign to at least send a surrogate to speak to voters at their events, said Ms. Ghori, of the Muslim Public Affairs Council.

Before the Virginia primary in February, some of the nation’s leading Muslim organizations nearly canceled an event at a mosque in Sterling because they could not arrange for representatives from any of the major presidential campaigns to attend. At the last minute, they succeeded in wooing surrogates from the Clinton and Obama campaigns by telling each that the other was planning to attend, Mr. Bray said. (No one from the McCain campaign showed up.)

Frustrations with Mr. Obama deepened the day after he claimed the nomination when he told the American Israel Public Affairs Committee that Jerusalem should be the undivided capital of Israel. (Mr. Obama later clarified his statement, saying Jerusalem’s status would need to be negotiated between Israelis and Palestinians.)

Osama Siblani, the editor and publisher of the weekly Arab American News in Dearborn, said Mr. Obama had “pandered” to the Israeli lobby, while neglecting to meet formally with Arab-American and Muslim leaders. “They’re trying to take the votes without the liabilities,” said Mr. Siblani, who is also president of the Arab American Political Action Committee.

Some Muslim supporters of Mr. Obama seem to ricochet between dejection and optimism. Minha Husaini, a public health consultant in her 30s who is working for the Obama campaign in Philadelphia, lights up like a swooning teenager when she talks about his promise for change.

“He gives me hope,” Ms. Husaini said in an interview last month, shortly before she joined the campaign on a fellowship. But she sighed when the conversation turned to his denials of being Muslim, “as if it’s something bad,” she said.

For Ms. Ghori and other Muslims, Mr. Obama’s hands-off approach is not surprising in a political climate they feel is marred by frequent attacks on their faith.

Among the incidents they cite are a statement by Mr. McCain, in a 2007 interview with Beliefnet.com, that he would prefer a Christian president to a Muslim one; a comment by Senator Hillary Rodham Clinton that Mr. Obama was not Muslim “as far as I know”; and a remark by Representative Steve King, Republican of Iowa, to The Associated Press in March that an Obama victory would be celebrated by terrorists, who would see him as a “savior.”

“All you have to say is Barack Hussein Obama,” said Arsalan Iftikhar, a human rights lawyer and contributing editor at Islamica Magazine. “You don’t even have to say ‘Muslim.’ ”

As a consequence, many Muslims have kept their support for Mr. Obama quiet. Any visible show of allegiance could be used by his opponents to incite fear, further the false rumors about his faith and “bin-Laden him,” Mr. Bray said.

“The joke within the national Muslim organizations,” Ms. Ghori said, “is that we should endorse the person we don’t want to win.”

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